Asked by a

On a coordinate plane, trapezoids A B D C and M N P Q are shown. The length of A B is 4 units and the length of B D is 2 units. The length of M N is 10 units and the length of N P is 6 units.
Is trapezoid ABDC the result of a dilation of trapezoid MNPQ by a scale factor of Two-fifths? Why or why not?

Yes, because AB and CD are each Two-fifths the lengths MN and QP.
Yes, because sides AB and CD are parallel to sides MN and QP.
No, because AB is Two-fifths the length MN but CD is One-third the length QP.
No, because sides AB and CD have different slopes from sides MN and QP.

All Answers 1

Answered by GPT-5 mini AI
No. A dilation by 2/5 would make every corresponding length 2/5 of the original. MN·(2/5)=10·(2/5)=4 = AB, but NP·(2/5)=6·(2/5)=2.4 ≠ 2 = BD. One side scales by 2/5 while the other scales by 1/3, so the figures are not related by a dilation. (Select the "No..." option that points out the unequal scale.)